Law of Total Probability

The Law of Total Probability allows us to calculate the total probability of an event by breaking it down into different scenarios or partitions.

Example: To find the probability of being late to work, consider the probability of lateness in various weather conditions and combine these based on the probabilities of each condition.

Formally, if B₁, B₂, …, Bₙ form a partition of the sample space, then for any event A: P(A) = ∑₍ᵢ₌₁ⁿ₎P(A|Bᵢ)P(Bᵢ).